My husband found a 1 1/2 in with head in and 2 in with it out turtle in the area he is building a new workshop in our backyard. We have woods behind us and there are a couple of lakes about a 1/4 mile away. I don't know what kind and have looked at your photos. Not sure if we should keep him untill he gets a bit bigger or if we should let him go. Don't know what to feed him or put him in either. He has some yellowish markings on his head, yellowish edge around his shell, beautiful designs on his shell, lots of little swirlies, and an ivory belly.
He might be a box turtle, yellow-bellied slider, painted turtle, or something like that. My page on turtle hatchlings is at
http://www.fishpondinfo.com/turtles/hatchling.htm and has sections on legalities and how to care for the turtle if you keep him. If there's a hinge on the bottom shell that lets him close his head in all the way, then it's a box turtle. My page on them is at
http://www.fishpondinfo.com/turtles/box.htm . I usually suggest releasing turtles near where they are found so that they can lead the natural life that they were meant to lead.